Viscosities, diffusion coefficients, and mixing times of intrinsic fluorescent organic molecules in brown limonene secondary organic aerosol and tests of the Stokes-Einstein equation

. Viscosities and diffusion rates of organics within secondary organic aerosol (SOA) remain uncertain. Using the bead-mobility technique, we measured the viscosities as a function of water activity (a w ) of SOA generated by the ozonolysis of limonene 20 followed by browning by exposure to NH 3 (referred to as brown limonene SOA or brown LSOA). These measurements together with viscosity measurements reported in the literature show that the viscosity of brown LSOA increases by 3-5 orders of magnitude as the a w decreases from 0.9 to approximately 0.05. In addition, we measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using rectangular area fluorescence recovery after photobleaching. Based on the diffusion measurements, as the a w decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic 25 fluorescent organic molecules decreases from 5.5∙10 -9 cm 2 s -1 to 7.1∙10 -13 cm 2 s -1 and the mixing times of intrinsic fluorescent organic molecules within 200 nm brown LSOA particles increases from 0.002 s to 14 s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short (< 1 hr) for a w and temperatures often found in the PBL. Since the diffusion coefficients and mixing times reported here correspond to SOA generated using a high mass loading ( ~ 1,000 µg m -3 ), biogenic SOA particles found in the atmosphere with mass loadings ≤ 10 µg m -3 are likely to have higher 30 viscosities and longer mixing times. These new measurements of viscosity and diffusion were used to test the accuracy of the Stokes-Einstein relation for predicting diffusion rates of organics within brown LSOA matrices. The results show that the Stokes-Einstein equation gives accurate predictions of diffusion coefficients of large organics within brown LSOA matrices when the viscosity of the matrix is as high as 10 2 to 10 4 Pa s. These results have important implications for predicting diffusion and mixing with SOA particles in the atmosphere. measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using a technique called rectangular area fluorescence recovery after photobleaching. These new data, combined with viscosity data that already exist in the literature for brown LSOA-water matrices, were used to test the accuracy of the Stokes-Einstein relation 90 for predicting diffusion rates of organics within SOA particles. We also used the measured diffusion coefficients to estimate mixing times of organics within 200 nm brown LSOA particles at RHs typically found in the planetary boundary layer (the region of the atmosphere from the surface to an altitude of up to 1 km). We focused on brown LSOA for the following reasons:


Introduction
Large amounts of volatile organic compounds, such as isoprene, limonene, and α-pinene from biogenic sources and aliphatic 40 and aromatic compounds from anthropogenic sources are released into the atmosphere. These compounds can be oxidized by a complex series of atmospheric reactions to form lower-volatility products that condense to form secondary organic aerosols (SOA) (Hallquist et al., 2009;Kanakidou et al., 2005). SOA makes up approximately 30-70% of the mass of atmospheric particles (Kanakidou et al., 2005;Jimenez et al., 2009). Due to the hygroscopic nature of SOA, an important component of SOA particles is water Hildebrandt Ruiz et al., 2015;Massoli et al., 2010). The amount of water in SOA 45 particles is determined by the relative humidity (RH); as the RH increases, the water activity (aw) (and hence water content) in SOA particles increases to maintain equilibrium with the gas phase. SOA particles can influence climate either directly by absorbing or scattering sunlight or indirectly by acting as cloud condensation nuclei (CCN) or ice nuclei (IN) (Kanakidou et al., 2005;Murray et al., 2010;Solomon, 2007;Wang et al., 2012). SOA particles can also influence air quality and public health (Baltensperger et al., 2008;Jang et al., 2006;Poschl and Shiraiwa, 2015;Shiraiwa et al., 2017b). 50 Despite the importance of SOA particles in climate and air quality, their physicochemical properties remain poorly understood (Hallquist et al., 2009). This leads to uncertainties when predicting the role of SOA particles in atmospheric chemistry, climate, and air quality (Hallquist et al., 2009;Shiraiwa and Seinfeld, 2012;Shrivastava et al., 2017a;Zaveri et al., 2014). One physicochemical property that remains poorly known is the rate of diffusion of organics within SOA particles (Liu et al., 55 2016;Shiraiwa et al., 2013;Shrivastava et al., 2017a;Ye et al., 2016). Information on diffusion rates is needed to predict the reactivity and photochemistry of SOA particles Davies and Wilson, 2015;Gržinić et al., 2015;Houle et al., 2015;Li et al., 2015;Lignell et al., 2014;Wang et al., 2015). Diffusion rates are also needed to predict the growth rates, size distributions, cloud condensation ability, and ice nucleating ability of SOA particles (Boyd et al., 2017;Huff Hartz et al., 2005;Murray et al., 2010;Perraud et al., 2012;Riipinen et al., 2011;Shiraiwa and Seinfeld, 60 2012;Solomon and (eds.), 2007;Taina et al., 2017;Wagner et al., 2017;Wang et al., 2012;Zaveri et al., 2014;Zaveri et al., 2018).

= 6
(1) where D is the diffusion coefficient of the diffusing species, is the Boltzmann constant, is the temperature, is the dynamic 70 viscosity and is the hydrodynamic radius of the diffusing species. Until now, the accuracy of the Stokes-Einstein relation for predicting diffusion rates of organics in SOA particles has not been quantified, leading to uncertainties when estimating diffusion rates from viscosity measurements. Motivated primarily by the food industry, there have been a few tests of the Stokes-Einstein relation for predicting diffusion rates of organics in organic-water matrices, such as saccharide-water matrices (Bastelberger et al., 2017;Champion et al., 1997;Chenyakin et al., 2017;Corti et al., 2008;Price et al., 2016). In these cases, the 75 matrices contained only two species (one organic and water), which is very different from SOA matrices that contain thousands of different species (Nozière et al., 2015).
In the future, researchers will likely continue to use viscosity data combined with the Stokes-Einstein relation to estimate diffusion rates of organics in SOA particles, because several techniques have been developed recently to measure the 80 viscosities of SOA matrices and proxies of SOA matrices Grayson et al., 2016;Lee et al., 2017;Marsh et al., 2017;Price et al., 2015;Reid et al., 2018;Renbaum-Wolff et al., 2013a;Song et al., 2015;Zhang et al., 2015). As a result, the accuracy of the Stokes-Einstein relation for predicting diffusion rates of organics in SOA particles needs to be quantified.
In the following, we measured the viscosities of brown limonene SOA (brown LSOA) as a function of aw using the bead-85 mobility technique. The brown LSOA is a product of exposure of white limonene ozonolysis SOA to ppb levels of ammonia vapour , and it is a model system for the formation of secondary brown carbon . In addition, we measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using a technique called rectangular area fluorescence recovery after photobleaching. These new data, combined with viscosity data that already exist in the literature for brown LSOA-water matrices, were used to test the accuracy of the Stokes-Einstein relation 90 for predicting diffusion rates of organics within SOA particles. We also used the measured diffusion coefficients to estimate mixing times of organics within 200 nm brown LSOA particles at RHs typically found in the planetary boundary layer (the region of the atmosphere from the surface to an altitude of up to 1 km). We focused on brown LSOA for the following reasons: first, brown LSOA contains light absorbing molecules that are also fluorescent (here referred to as intrinsic fluorescent organic molecules) and capable of rapid photobleaching (Lee et al., 2013). These intrinsic fluorescent organic molecules offer a key 95 advantage because one can measure diffusion coefficients within brown LSOA using rectangular area fluorescence recovery after photobleaching without the need to add a foreign tracer fluorescent molecule to the SOA matrix. Second, limonene accounts for roughly 10 % of the global emissions of monoterpenes (and is thus an important source of SOA in the atmosphere) (Kanakidou et al., 2005;Sindelarova et al., 2014).

Generation of brown LSOA
Brown LSOA was produced at the University of California-Irvine (UCI) following the procedure outlined in Hinks et al. (2016). First, particles consisting of limonene secondary organic material (LSOA) were generated in a 20 L flow tube by dark ozonolysis of d-limonene. Mixing ratios of ozone and d-limonene (97% Sigma-Aldrich) were both 10 ppm prior to reaction. Ozone was produced externally to the flow tube by an electric discharge in pure O2 (Ultra High Purity, Airgas). After 105 the ozonolysis reaction, the mass concentration of LSOA particles within the flow tube was approximately 1,000 µg/m 3 . At the exit of the flow tube, the carrier gas and LSOA particles were passed through a charcoal denuder to eliminate excess ozone and gas-phase organics, followed by collection of the LSOA particles on hydrophobic slides (Hampton Research; Aliso Viejo, CA, USA) using a Sioutas impactor with a single stage "D" (0.25 μm cut point at 9 SLM collection flow rate). After LSOA production, the hydrophobic slides containing the LSOA were placed within a small glass petri dish, which was left floating 110 on the surface of a solution of 0.1 M ammonium sulfate (>99 %, EMD) in a larger, covered petri dish. Over a period of three to five days, the ammonia vapour in equilibrium with the ammonium sulfate solution (concentration estimated to be 300 ppb NH3 using the Extended AIM Aerosol Thermodynamics Model II) (Clegg et al., 1998) reacted with the fresh LSOA forming a visible brown colour. After production of the brown LSOA, the samples were shipped to the University of British Columbia for viscosity and diffusion coefficient measurements. 115

Viscosity measurements
The viscosities of brown LSOA particles were determined at aw of approximately 0.7, 0.8 and 0.9, using the bead mobility technique (Renbaum-Wolff et al., 2013b). At lower aw, the viscosities were too high for measurements with this technique, but viscosity for the same brown LSOA at aw of 0.05 and 0.3 are available from previous poke-flow measurements by Hinks et al. 120 (2016). Small particles (5-50 µm in diameter) of brown LSOA were deposited on fluorinated glass slides (Knopf, 2003)  Once the fluorinated glass slides containing the brown LSOA particles were placed in the flow cell, a constant flow (1100 to 1200 sccm) of humidified nitrogen gas (Praxair, ultrapure) was passed over the brown LSOA particles, which caused a shear stress on the surface of the particles and circulation of the beads within the particles. The velocity of the beads was determined using an optical microscope (Zeiss Axio Observer). For each aw studied, the speed of 7 to 16 beads in 2 to 5 brown LSOA 135 droplets was measured and the bead speed was averaged. Once determined, the velocity of the beads was converted to viscosity using a calibration curve based on sucrose-water particles and glycerol-water particles from Grayson et al. (2017) . Prior to measuring the velocity of the beads in an experiment, the brown LSOA particles were equilibrated with the RH within the flow cell for approximately 20 min, which should be long enough to ensure equilibration (Section S1).

Generation of thin films of brown LSOA with a known aw for the diffusion coefficient measurements
Brown LSOA contains light absorbing molecules that are also fluorescent and easily photobleachable (Lee et al., 2013).
Diffusion coefficients of these intrinsic fluorescent organic molecules were determined using rectangle area fluorescent recovery after photobleaching (discussed below). For this technique, thin films (20-90 µm thick) containing brown LSOA with 145 a known aw were needed. To produce thin films of brown LSOA with a known aw, particles of brown LSOA with diameters of 50-200 µm were deposited on hydrophobic slides from the samples received from the UCI using the tip of a needle (BD Precision GlideTM Needle, 0.9 mm x 40 mm). The super-micrometer brown LSOA particles were then located within a flow cell or sealed glass jar with controlled RH to set the aw within the brown LSOA (at equilibration, aw within the brown LSOA equals RH/100). The times used to condition the brown LSOA particles to the controlled RH are given in Table S1, ranging 150 from 17 min to 1.5 months, and discussed in Section S1. After equilibration, the brown LSOA particles were sandwiched between two hydrophobic glass slides to generate a thin film of brown LSOA with a thickness of 20-90 µm. Assembly of the films occurred within a glove bag that had a RH set to match the RH used for conditioning the brown LSOA particles in order to ensure the aw within the LSOA did not change during assembly of the films. The thickness of the films was controlled by aluminium spacers inserted between the two hydrophobic glass slides prior to assembly. After assembly, the brown LSOA 155 within the thin films were isolated from the surrounding atmosphere using a layer of vacuum grease around the perimeter of the films. For further details, see Chenyakin et al. (2017).

Measurements of diffusion coefficients
Fluorescence recovery after photobleaching (FRAP) has often been used to determine diffusion rates of fluorescent molecules in biological samples such as in the cytoplasm and nuclei of cells (Axelrod et al., 1976;Deschout et al., 2010;Jacobson et al., 160 1976;Meyvis et al., 1999;Seksek et al., 1997). To determine diffusion coefficients of the intrinsic fluorophores in the brown LSOA, we used a version of FRAP, referred to as rectangular area fluorescence recovery after photobleaching (rFRAP) (Deschout et al., 2010). In rFRAP, a rectangular region of a thin film containing fluorescent molecules is photobleached with The rFRAP measurements were conducted with a laser scanning confocal microscope (Zeiss Axio Observer LSM 5 10 MP) with a low numerical aperture objective (Zeiss EC-Plan Neofluar 10x, 0.3 numerical aperture) to ensure near uniform 170 photobleaching in the z-direction. One-dimensional scanning with a pixel dwell of 2.56 µs and an image scan time of 1.57 s was used. The images were acquired with 512x512 pixels with a pinhole set to 80 µm. The scanning laser power was varied between 17.0 to 42.6 µW depending on the fluorescence of the sample. In order to achieve a bleach depth (decrease in fluorescence intensity) of 30-50 %, as suggested by Deschout et al. (2010) for rFRAP experiments, the laser power for photobleaching was varied between 93 and 297 µW, depending on the sample (Deschout et al., 2010). 175 A rectangular area was used for photobleaching with length (x) and width (y), with smaller areas for longer diffusion times.
The image sizes used in the rFRAP experiments were chosen in relation to the bleach size with larger image sizes used for larger bleach sizes. For example, at aw≥0.8, photobleached areas of 20 µm by 20 µm and image sizes of 199.6 µm by 199.6 µm were used, while at aw=0.33, photobleached areas of 5 µm by 5 µm and 3 µm by 3 µm and image sizes of 30 µm by 30 µm 180 were used. All rFRAP experiments were carried out at a temperature of 294.5±1.0 K. Shown in Figure 1 are examples of images of brown LSOA films with aw of 0.33, 0.6 and 0.9 recorded during rFRAP experiments.

Extraction of diffusion coefficients
Based on Fick's second law of diffusion, Deschout et al. (2010) developed the following equation to describe the fluorescence intensities in thin films after photobleaching a rectangular area with a confocal microscope (Deschout et al., 2010): 185 )], where F(x, y, t) is the fluorescence intensity at coordinate (x,y) and time t after photobleaching, F 0 (x, y) is the fluorescence intensity at coordinate (x,y) prior to photobleaching, K 0 is the effective bleach depth, which describes the decrease of the fluorescence intensity within the photobleached area, l x and l y are the lengths of the photobleached area, r is the lateral resolution of the microscope, and D is the diffusion coefficient of the fluorescent molecules. The parameter w(D, t, r) is given 190 by the following equation: w(D, t, r) = r 2 + 4Dt.
(3) In a first step of the analysis for the extraction of diffusion coefficients, the images recorded after photobleaching were normalized to an image recorded prior to photobleaching using the open source program ImageJ (Schneider et al., 2012). The 195 resolution of the images was changed from 512x512 pixels to 128x128 pixels by averaging to reduce the noise. Then, Eq. 2 was used to extract ( , , ) from each image. In the fitting procedure used to extract ( , , ), 0 as well as a normalization factor were left as free parameters. Next, ( , , ) was plotted as a function of and a straight line was fit to the data. The diffusion coefficient, , was calculated from the slope of the straight line using a linear fit with Eq. (3). Examples of plots of ( , , ) vs t are shown in Figure 2. 200 Equation 2 assumes that the only mechanism for recovery in the photobleached region is diffusion of unbleached molecules.
The spontaneous recovery of the fluorescence signal without diffusion, referred to as reversible photobleaching, has been observed in previous studies at short timescales (Sinnecker et al., 2005;Stout and Axelrod, 1995;Verkman, 2003). To determine if this process occurred during our diffusion measurements with brown LSOA, a separate set of experiments was carried out.
Particles of brown LSOA (40 to 90 µm in diameter) were conditioned to an aw of 0.6 and the entire particle was photobleached 205 until the fluorescence intensity decreased by between 17 and 47%. The photobleaching was performed across the entire particle in order to rule out fluorescence intensity recovery due to diffusion of fluorescent molecules. Within the first five seconds after photobleaching a small amount of the fluorescent signal recovered (1-3 % of the photobleached signal), which we attribute to reversible photobleaching. To ensure this process did not impact our diffusion measurements, the data recorded during the first five seconds after photobleaching in the rFRAP experiments were not included when determining diffusion coefficients. 210 Possible heating of the sample during photobleaching by the laser was not expected to impact the diffusion measurements since local heating during photobleaching should be dissipated to the surroundings much faster than the time of the diffusion measurements. Nevertheless, to support this expectation, two experiments were carried out with different laser intensities but on the same sample conditioned to an aw to 0.9. A laser intensity of 139.9 µW was used for a bleach depth of 20% and a laser intensity of 330 µW was used for a bleach depth of 50%. Within uncertainty, the diffusion coefficients determined with both 215 bleach depths were in agreement: (2.5±0.5)•10 -9 cm 2 s -1 was obtained for a laser intensity of 139.9 µW and (2.8±0.1)•10 -9 cm 2 s -1 for a diffusion coefficient was obtained for a laser intensity of 330 µW (uncertainties correspond to 95 % confidence intervals). is the normalized fluorescence signal, 225 and T0 is the transmittance prior to the photobleaching process. Equation 4 is derived in Section S2. After the normalized concentrations were calculated, they were used in Eq. 2 in place of the normalized fluorescence signal. Note, the application of Eq. 4 to account for non-linearity between the fluorescence signal and concentration changed the diffusion coefficients by less than the uncertainties in the measurements. Figure 3 shows the viscosity of brown LSOA as a function of aw measured with the bead-mobility technique. For comparison, the known viscosity of pure water and the viscosity of brown LSOA measured previously using the poke-and-flow technique are also included (Hinks et al., 2016). Overall, Figure 3 shows that the viscosity increases by 3-5 orders of magnitude as the aw decreases from 0.9 to approximately 0.05. An increase in viscosity with a decrease in aw is expected due to the plasticizing 235 effect of water Power et al., 2013;Zobrist et al., 2011). A liquid has a viscosity of < 10 2 Pa•s, a semisolid has a viscosity of 10 2 and 10 12 Pa•s, and an amorphous solid has a viscosity of > 10 12 Pa•s Mikhailov et al., 2009;. Based on Figure 3, the brown LSOA studied here can be considered as a liquid above a aw of 0.7, and as a semisolid at aw below roughly 0.5.

Diffusion coefficients and mixing times of intrinsic fluorophores in brown limonene SOA 240
Figure 4(a) shows the measured diffusion coefficients of the intrinsic fluorophores in brown LSOA as a function of aw. The average diffusion coefficient decreases from 5.5•10 -9 cm 2 /s to 7.1•10 -13 cm 2 /s as the aw decreases from 0.9 to 0.33. The strong dependence on aw is due to the plasticizing effect of water as mentioned above Power et al., 2013;Zobrist et al., 2011). Also included in Figure 4 (secondary y-axis) is the mixing time of the intrinsic fluorophores by molecular diffusion within a 200 nm brown SOA particle based on the measured diffusion coefficients. Mixing times were calculated 245 with the following equation (Seinfeld and Pandis, 2016;: where is the diameter of the particle and the measured diffusion coefficient of the intrinsic fluorophore. The mixing time is the time after which the concentration of the diffusing molecules at the centre of the particle deviates by less than 1/e from the equilibrium concentration . Based on the measured diffusion coefficients, for the brown LSOA 250 studied here mixing times of the organics within 200 nm particles range from 0.002 s to 14 s for aw from 0.9 to 0.33. Figure 4 is the frequency distributions of aw (Panel b) and temperatures (Panel c) found in the planetary boundary layer (PBL) for the months of January and July. We calculated these frequency distributions using GEOS-Chem version v10-  (Pye et al., 2010), which was driven by 6-hr average GEOS-5 meteorology fields. Following Maclean et al. (2017), when 255 determining the frequency distributions of aw and temperatures within the PBL, we only included grid cells in a column up to the top of the PBL if the monthly averaged concentrations of organic aerosol (OA) were > 0.5 g m -3 at the surface, based on GEOS-Chem version v10-01 (Pye et al., 2010). We excluded cases when OA concentrations were < 0.5 g m -3 at the surface since these concentrations are not expected to be important for climate or health. OA concentrations were > 0.5 g m -3 in all but one of the previous surface measurements of OA at remote locations (Spracklen et al., 2011). 260 Figure 4(b) shows that the aw in the PBL is most often  0.33 when the organic mass concentrations are higher than 0.5 µg m -3 at the surface. Figure 4(c) shows that the temperature in the PBL is often within 5 K of the temperature used in our experiments (294.5 K). Based on Figure 4, mixing times of intrinsic fluorophore in the brown LSOA studied here are often short (< 1 h) for the aw and temperatures most often found in the PBL when the organic mass concentrations are higher than 265 0.5 µg m -3 .

Also shown in
The diffusion coefficients and mixing times reported here correspond to brown LSOA generated using mass concentrations of 1,000 µg m -3 in a flow reactor. For some types of SOA (SOA from ozonolysis of α-pinene, limonene, 3-hexenyl acetate and 3-hexen-1-ol) the viscosity of the SOA increases as the mass concentration used to generate the SOA decreases (Grayson et 270 al., 2016;Jain et al., 2018). Since mass concentrations of biogenic SOA particles found in the atmosphere are most often ≤ 10 µg m -3 (Spracklen et al., 2011) the values reported here likely represent the lower limit for the viscosities and upper limit for the diffusion coefficients. Additional studies are needed to determine diffusion coefficients and mixing times for more atmospherically relevant mass concentrations. In addition, the brown LSOA were generated using a ratio of limonene to ozone ~1, which suggests than not all double bonds in limonene were oxidized. Additional studies are also needed to determine if 275 diffusion coefficients in brown LSOA are sensitive to the extent of oxidation of LSOA molecules. Ye et al. (2018) studied the timescale for mixing of organics from toluene oxidation within limonene SOA particles using mass spectrometry (Ye et al., 2018). In these studies, the limonene SOA particles were generated with mass concentration of 16-22 µg m -3 . Based on the studies by Ye et al. (2018) the mixing times of organics within limonene SOA particles is on the order 280 of 3-4 hr for RH values ranging from 10 to 30%, with little evidence for an RH dependence. At 33% RH, we calculate a mixing time of approximately 14 s. This corresponds to a difference in diffusion coefficients of a factor of roughly 1000. A possible explanation for the apparent difference between the current results and the results reported by Ye et al. (2018) is the difference in the mass concentrations used to generate the SOA, and the low extent of oxidation of LSOA compounds, as discussed above. 285 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-899 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 September 2018 c Author(s) 2018. CC BY 4.0 License.

Comparison between measured diffusion coefficients and Stokes-Einstein predictions
Shown in Figure 5 are the measured diffusion coefficients and predicted diffusion coefficients based on viscosity measurements and the Stokes-Einstein relation. The viscosity measurements include our new bead-mobility viscosity results ( Figure 3) and previous poke-flow viscosity measurements by Hinks et al. (2016), as well as viscosity measurements of pure 290 water for comparison (Crittenden et al., 2012;Hinks et al., 2016). To predict diffusion coefficients from the viscosity measurements and the Stokes-Einstein equation, the average dimension of the intrinsic fluorophores is needed. The exact molecular identities of the chromophores and fluorophores in brown LSOA is not known. Previous studies suggest that there is a distribution of chromophores with a broad range of molecular weights of the order of 500 g/mol (Nguyen et al., 2013). Therefore, we tested a range of molecular weights from 300 to 800 g/mol, corresponding to hydrodynamic radii from 4.5 to 295 6.2 Å with an assumed density of 1.3 g/cm 3 (Saathoff et al., 2009), and an assumed spherical geometry of the intrinsic fluorophores. Figure 5 shows that the difference between the measured and predicted diffusion coefficients is less than the uncertainty of the measurements for diffusion coefficients as small as roughly 10 -12 cm 2 s -1 , which corresponds to a viscosity of between 4•10 2 to 300 1.2•10 4 Pa• s, based on Figure 4. This conclusion is consistent with most previous studies that have investigated the accuracy of the Stokes-Einstein relation for predicting diffusion coefficients of large organic molecules in organic-water mixtures. For example, Chenyakin et al. (2017), Champion et al. (1997, and Price et al. (2016) showed that the Stokes-Einstein relation predicts diffusion coefficients of large organics in sucrose-water solution consistent with measurements (i.e., within the uncertainty of the measurements) when the viscosity is ≲ 1•10 4 Pa•s (Champion et al., 1997;Chenyakin et al., 2017;Price et al., 305 2016). In contrast, Longinotti and Corti (2007) and Corti et al. (2008) found disagreement between measured and predicted diffusion coefficients of large organics in organic-water solutions at slightly lower viscosities (Corti et al., 2008;Longinotti and Corti, 2007).

Summary and conclusion 310
One physicochemical property of SOA particles that remains poorly understood is diffusion rates of representative organics within SOA particles. To estimate diffusion rates of organics in realistic models for SOA particles, we (as well as other researchers) have used viscosity measurements together with the Stokes-Einstein relation. Until now, the accuracy of the Stokes-Einstein relation for predicting diffusion coefficients of organics in SOA particles had not been quantified, leading to uncertainties when estimating diffusion rates from viscosity measurements. In this study, we measured the viscosity of brown 315 LSOA using the bead mobility technique. From these viscosity values, we calculated diffusion coefficients of large organic molecules in brown LSOA. These calculated diffusion coefficient values were compared to diffusion coefficients of large organic molecules that were measured directly in brown LSOA using fluorescence recovery after photobleaching. We found Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-899 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 September 2018 c Author(s) 2018. CC BY 4.0 License. that the Stokes-Einstein relation gives diffusion coefficients within the uncertainty of the measurements for brown LSOA matrices with viscosities between 0.2 Pa• s and 1.2•10 4 Pa• s. 320 In addition, mixing times in a 200 nm sized brown LSOA particle were calculated based on the measured diffusion coefficients.
Mixing times were found to vary between 0.001 s at an aw of 0.9 and 14 s at an aw of 0.3. These results suggest that the mixing times of large organics in the brown LSOA studied here are short (< 1 h) for aw and temperatures often found in the PBL.
However, since the mixing times reported here correspond to brown LSOA generated using mass loadings of 1,000 µg m -3 , 325 the mixing times are likely to be longer in ambient biogenic SOA particles typically found at mass loadings below 10 µg m -3 (Spracklen et al., 2011). Additional studies are needed using more atmospherically relevant mass concentrations, as well as utilizing a range of oxidation conditions from "fresh" to "highly-aged" SOA.